TABLE B-8.-CHINA: REPORTED AND ESTIMATED GROSS VALUE OF INDUSTRIAL OUTPUT, BY REGION, 1952, 1957,

Note: Components may not add to the total because of rounding. For those provinces for which the gross value of industrial production was not reported or could not be derived, estimates were made by the method described in the source cited.

Source: Robert Michael Field, Nicholas R. Lardy, John Philip Emerson, "A Reconstruction of the Gross Value of Industrial Output by Province in the People's Republic of China: 1949-73," U.S. Department of Commerce, forthcoming.

APPENDIX C

THE CALCULATION OF INDEX NUMBERS FROM INCOMPLETE DATA 23

I. Introduction

In economics, the measurement of changes in output over time on the basis of incomplete data is a nearly universal problem: observations from some series are almost always missing. Soviet economic data, for example, are more complete for the last year of a 5-year plan period than for other years; in the United States, data are more complete for years in which a census of manufactures has been taken; and in some less developed countries, data are published only sporadically. The problem is how to calculate index numbers that squeeze the most information out of the data that are available.

Procedures to calculate index numbers from incomplete data that were devised by Kaplan and Moorsteen in 1960 and by Field in 1974 are described in sections II and III, respectively. The Field index is a generalization of the KaplanMoorsteen method. To make the two procedures clear, indexes are calculated from the hypothetical data presented in table C-1.

In their work on Soviet industry, Kaplan and Moorsteen devised an ingenious method for dealing with the problem of incomplete data. They defined three indexes, as follows:

A benchmark index is a Laspeyres index calculated for all years in which output data are available for every commodity. In the sample problem, the benchmark index is calculated for years 1 and 5.

23 Reprinted from Robert Michael Field, Nicholas R. Lardy, and John Philip Emerson, A Reconstruction of the Gross Value of Industrial Output in the People's Republic of China: 1949-73, U.S. Department of Commerce, forthcoming.

24 Norman M. Kaplan and Richard H. Moorsteen, Indexes of Soviet Industrial Output, Santa Monica, 1960, pp. 61-68.

An interpolating index is a Laspeyres index calculated for the years between benchmark years. It is based on those commodities for which output data are available in every year. A separate index is calculated between each successive pair of benchmark years. In the sample problem, the interpolating index is calculated from output series B, D, and E.

An extrapolating index is a Laspeyres index calculated for the years after the last benchmark year. It is based on those commodities for which output data are available in every year. In the sample problem, the extrapolating index is calculated from output series D, E, and F.

The Kaplan-Moorsteen index for the years between benchmark years is calculated recursively from these indexes according to the formula:

where I is the interpolating index, and a and B are the average annual rates of growth of the benchmark and interpolating indexes, respectively. The procedure for extrapolation is analogous.

Indexes calculated by the Kaplan-Moorsteen method from the sample data are presented in table C-2. The final index has two desirable properties: The year-toyear pattern of change is the same as that shown by the interpolating and extrapolating indexes, and the average annual rates of growth between benchmark years are the same as those shown by the benchmark index. However, the index does not make use of all the data that are available. The interpolated portion of the index does not make use of series A or F, and the extrapolated portion does not make use of series B or C.

How can the information not used in the interpolating and extrapolating indexes be captured in an aggregate index? Recasting the form of the Kaplan-Moorsteen index gives an insight into the problem. If the index for the base year is KM。, then the index for the jth year is:

KM;= (1+a)' (†)KM.

and the relationship between the years j and i is:

But the ratio 1/1, is based only on those series that are complete and does not necessarily take full advantage of all the data that are available.

The best statement of the relationship between output in the years j and i is the link relative:

where P and Q are price and quantity, respectively, n is the number of output series, and 8 is an indicator function. The function is defined as:

The link relative r,, is the ratio of the output of those commodities for which output data are available both in year i and in year j.

The Field index is calcu lated between successive benchmark years from a complete set of link relatives. First, because the series for which output data are available may not be growing at the same rate as aggregate output, the link relatives are adjusted in a manner analogous to that used by Kaplan and Moorsteen to adjust their in terpolating i ndex. The adjusted link relative is:

where a and v1, are average annual rates of growth. Specifically, if years g and h are benchmark years,

a is the rate of growth for all commodities between benchmark years g and h, and Yij is the rate of growth of those commodities for which output data are available both in year i and in year j. a has to be calculated only once, but y;; must be calculated separately for each link relative.

Finally, the index Î, is estimated by least squares from the following equation:

Taking the logarithms of both sides of the equation yields:

The sum of the squares of log e; is minimized, subject to the constraint that the estimated index equals the benchmark index in benchmark years. If years g and h are benchmark years, minimize

where Y, and Y are the values of the benchmark index in years g and h. The partial derivatives of the objective function are a system of simultaneous linear equations whose solution is the Field index.

The equations for estimating the Field index between years 1 and 5 of the sample problem are as follows:

The procedure for extrapolation is analogous to that described above for interpolation. However, two points should be noted. First, if there are more than 2 years for which the data are complete, the selection of the benchmark years on which to base the adjustment of the link relatives offers a choice. It would seem logical that one benchmark should be the last complete year, but the selection of the other is arbitrary, and the year selected may affect the rate of growth shown by the index. Second, adding output data for a subsequent year may change the index numbers for the years since the last benchmark. Because the original estimate was based on incomplete data, and because the output data for the additional year give new information against which to judge performance in the earlier years, the result is reasonable.

The Field index calculated from the sample data is presented in table C-3 and compared with the Kaplan-Moorsteen index. The Field index has several desirable properties in addition to using all of the data. First, if the data are complete, the index is the same as a Laspeyres index. Second, if some of the series are missing but the remaining series are complete, the index is the same as the KaplanMoorsteen index. Third, the index can be calculated even if there are no series that are complete. And last, the index can be calculated without complete data for benchmark years. If there are not 2 benchmark years, the index can be derived from the unadjusted link relatives.

TABLE C-3-ALTERNATIVE INDEXES CALCULATED FROM HYPOTHETICAL DATA

CHINA'S INDUSTRIAL SYSTEM

By THOMAS G. RAWSKI

I. INTRODUCTION

China's achievements in such diverse areas as nuclear weaponry, satellite technology, rural electrification, chemical fertilizer production and most recently, petroleum development illustrate the significance of industrial advance since 1949. Although the paucity of statistical information leads to differences among various estimates of industrial growth, all observers agree that output of factories, mines, and utilities has advanced at a rapid, though decelerating pace since 1949. My own studies indicate that in terms of 1952 prices, the average annual growth rate of industrial gross output value since 1952 falls within the range of 12 to 14 percent.' China's achievements compare favorably with industrial performance in other large developing nations such as Brazil and India, particularly since these countries have enjoyed freer access to foreign assistance, expertise and technology than has the People's Republic.

This impressive record raises many questions about the nature and evolution of industrial planning and factory management in the People's Republic. Who formulates annual plans? What relations exist among workers, factory executives and economic planners? What changes have occurred in industry since the 1950's? Could China benefit from the type of economic reforms which have recently appeared in the European socialist countries? This essay approaches these issues by discussing the origins of China's industrial system, its evolution. since the early 1950's, and the efficiency of industrial operations.2

II. THE SPREAD OF STATE CONTROL AND PRODUCTION PLANNING

China's system of industrial planning was not born overnight. The spread of central economic control was a gradual process, and it is only with the ratification of China's First Five-Year Plan (FFYP) in mid-1955, over 2 years after its formal beginning in January 1953, that we can begin to speak of an integrated industrial system and policy rather than collections of ad hoc production orders and investment projects.

1 Thomas G. Rawski, "Chinese Industrial Production, 1952-1971," Review of Economics and Statistics 55.2 (1973), pp. 169-181. The use of a later price base would lower the esti mated growth rate, but changing from gross to net output would raise the rate of growth. For alternative estimates of industrial growth, see Robert M. Field's contribution to this volume.

2 Previous studies of China's industrial system include Ishikawa Shigeru, Chugoku ni okeru shihon chikuseki kikō (The Mechanism of Capital Accumulation in China) (Tokyo, 1960); Audrey Donnithorne, China's Economic System (London, 1967); papers by Kang Chao and Dwight H. Perkins in Alexander Eckstein et al. eds.. Economic Trends in Communist China (Chicago, 1968); Barry M. Richman, Industrial Society in Communist China (N.Y., 1969) and Christopher Howe, Wage Patterns and Wage Policy in Modern China, 1919-1972 (Cambridge, England, 1973).